Question

PLEASE HELP I WILL GIVE POINTS AND BRAINLIEST AWAY

Answer 1

Answer:

g(x) = $x^2$ - 3

Step-by-step explanation:

Looking at the red dotted line, we see that it looks the exact same as the blue graph except that it is a few units lower.

Since the graph of g is moved vertically (down 3 units) from f, we know that this is a vertical transformation. So, we write the change to the entire function: g(x) = f(x) - 3

Now, what is f(x)? The graph of the generic quadratic $x^2$ is f(x). This is a graph that I highly recommend you memorize as it will definitely come in handy later on.

So, g(x) = f(x) - 3 = $x^2$ - 3.

We can check by plugging in the point (2, 1) that is on the graph of g and see if it works:

1 =? 2^2 - 3

1 =? 4 - 3

1 = 1

This works, so we know we're right.

Hope this helps!

Answer 2

Answer:

g(x) = x^2 - 3.

Step-by-step explanation:

f(x)  = x^2  because it goes through the origin and we can check the points (-1,1) and (1, 1) and (-2 4) and (2,4) which the curve passes through. They all satisfy f(x) = x^2. This graph is worth committing to memory. Note that it is symmetrical about the y-axis.

g(x) is the function f translated down 3 units so:

g(x) = x^2 - 3.